LMFDB - Embedded newform 441.2.w.a.251.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 11]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.10
Character	$\chi$	$=$	441.251
Dual form			441.2.w.a.188.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00441089 - 0.00351757i) q^{2} +(-0.445035 - 1.94982i) q^{4} +(-1.95912 - 0.943460i) q^{5} +(2.55289 + 0.694800i) q^{7} +(-0.00979136 + 0.0203320i) q^{8} +O(q^{10})$	\(q+(-0.00441089 - 0.00351757i) q^{2} +(-0.445035 - 1.94982i) q^{4} +(-1.95912 - 0.943460i) q^{5} +(2.55289 + 0.694800i) q^{7} +(-0.00979136 + 0.0203320i) q^{8} +(0.00532276 + 0.0110528i) q^{10} +(-1.56142 - 1.24519i) q^{11} +(-1.10775 - 0.883399i) q^{13} +(-0.00881652 - 0.0120447i) q^{14} +(-3.60370 + 1.73545i) q^{16} +(0.751799 - 3.29385i) q^{17} -6.30461i q^{19} +(-0.967708 + 4.23980i) q^{20} +(0.00250721 + 0.0109848i) q^{22} +(-7.96285 + 1.81747i) q^{23} +(-0.169433 - 0.212462i) q^{25} +(0.00177874 + 0.00779316i) q^{26} +(0.218614 - 5.28690i) q^{28} +(-5.47364 - 1.24932i) q^{29} +5.21141i q^{31} +(0.0660021 + 0.0150646i) q^{32} +(-0.0149024 + 0.0118843i) q^{34} +(-4.34589 - 3.76975i) q^{35} +(1.55054 - 6.79337i) q^{37} +(-0.0221769 + 0.0278090i) q^{38} +(0.0383648 - 0.0305949i) q^{40} +(9.97587 + 4.80413i) q^{41} +(0.0684189 - 0.0329488i) q^{43} +(-1.73302 + 3.59865i) q^{44} +(0.0415164 + 0.0199932i) q^{46} +(3.46380 - 4.34347i) q^{47} +(6.03450 + 3.54750i) q^{49} +0.00153314i q^{50} +(-1.22949 + 2.55306i) q^{52} +(0.739555 - 0.168799i) q^{53} +(1.88422 + 3.91261i) q^{55} +(-0.0391230 + 0.0451023i) q^{56} +(0.0197491 + 0.0247646i) q^{58} +(9.30068 - 4.47897i) q^{59} +(7.51004 + 1.71412i) q^{61} +(0.0183315 - 0.0229870i) q^{62} +(4.98744 + 6.25405i) q^{64} +(1.33675 + 2.77580i) q^{65} -8.97651 q^{67} -6.75700 q^{68} +(0.00590892 + 0.0319149i) q^{70} +(14.3180 - 3.26798i) q^{71} +(2.21540 - 1.76672i) q^{73} +(-0.0307354 + 0.0245107i) q^{74} +(-12.2929 + 2.80577i) q^{76} +(-3.12098 - 4.26371i) q^{77} -5.29436 q^{79} +8.69740 q^{80} +(-0.0271036 - 0.0562813i) q^{82} +(1.21293 + 1.52097i) q^{83} +(-4.58047 + 5.74373i) q^{85} +(-0.000417688 - 9.53346e-5i) q^{86} +(0.0406057 - 0.0195547i) q^{88} +(-4.85674 - 6.09016i) q^{89} +(-2.21417 - 3.02489i) q^{91} +(7.08749 + 14.7173i) q^{92} +(-0.0305569 + 0.00697441i) q^{94} +(-5.94815 + 12.3515i) q^{95} +0.0843849i q^{97} +(-0.0141390 - 0.0368744i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4}+O(q^{10}) $ 120 * q + 24 * q^4	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.00441089	−	0.00351757i	−0.00311897	−	0.00248730i	0.621929	−	0.783074i	$-0.286349\pi$
$2$	−0.00441089	−	0.00351757i	−0.00311897	−	0.00248730i	−0.625048	+	0.780586i	$0.714921\pi$
$3$		0			0
$3$		0			0
$4$	−0.445035	−	1.94982i	−0.222517	−	0.974912i
$5$	−1.95912	−	0.943460i	−0.876143	−	0.421928i	−0.0589288	−	0.998262i	$-0.518768\pi$
$5$	−1.95912	−	0.943460i	−0.876143	−	0.421928i	−0.817214	+	0.576334i	$0.804483\pi$
$6$		0			0
$7$	2.55289	+	0.694800i	0.964902	+	0.262610i
$7$	2.55289	+	0.694800i	0.964902	+	0.262610i
$8$	−0.00979136	+	0.0203320i	−0.00346177	+	0.00718844i
$9$		0			0
$10$	0.00532276	+	0.0110528i	0.00168320	+	0.00349521i
$11$	−1.56142	−	1.24519i	−0.470786	−	0.375439i	0.359166	−	0.933274i	$-0.383061\pi$
$11$	−1.56142	−	1.24519i	−0.470786	−	0.375439i	−0.829952	+	0.557834i	$0.811633\pi$
$12$		0			0
$13$	−1.10775	−	0.883399i	−0.307234	−	0.245011i	0.457719	−	0.889097i	$-0.348667\pi$
$13$	−1.10775	−	0.883399i	−0.307234	−	0.245011i	−0.764953	+	0.644086i	$0.777238\pi$
$14$	−0.00881652	−	0.0120447i	−0.00235631	−	0.00321907i
$15$		0			0
$16$	−3.60370	+	1.73545i	−0.900926	+	0.433863i
$17$	0.751799	−	3.29385i	0.182338	−	0.798875i	−0.798176	−	0.602425i	$-0.794201\pi$
$17$	0.751799	−	3.29385i	0.182338	−	0.798875i	0.980514	−	0.196450i	$-0.0629414\pi$
$18$		0			0
$19$		−	6.30461i		−	1.44638i	−0.690651	−	0.723188i	$-0.742676\pi$
$19$		−	6.30461i		−	1.44638i	0.690651	−	0.723188i	$-0.257324\pi$
$20$	−0.967708	+	4.23980i	−0.216386	+	0.948049i
$21$		0			0
$22$	0.00250721	+	0.0109848i	0.000534539	+	0.00234197i
$23$	−7.96285	+	1.81747i	−1.66037	+	0.378969i	−0.946852	−	0.321669i	$-0.895756\pi$
$23$	−7.96285	+	1.81747i	−1.66037	+	0.378969i	−0.713517	+	0.700637i	$0.752899\pi$
$24$		0			0
$25$	−0.169433	−	0.212462i	−0.0338865	−	0.0424924i
$26$	0.00177874	+	0.00779316i	0.000348839	+	0.00152836i
$27$		0			0
$28$	0.218614	−	5.28690i	0.0413141	−	0.999130i
$29$	−5.47364	−	1.24932i	−1.01643	−	0.231994i	−0.318320	−	0.947983i	$-0.603118\pi$
$29$	−5.47364	−	1.24932i	−1.01643	−	0.231994i	−0.698111	+	0.715990i	$0.745976\pi$
$30$		0			0
$31$			5.21141i			0.935998i	0.883729	+	0.467999i	$0.155025\pi$
$31$			5.21141i			0.935998i	−0.883729	+	0.467999i	$0.844975\pi$
$32$	0.0660021	+	0.0150646i	0.0116676	+	0.00266306i
$33$		0			0
$34$	−0.0149024	+	0.0118843i	−0.00255575	+	0.00203814i
$35$	−4.34589	−	3.76975i	−0.734590	−	0.637203i
$36$		0			0
$37$	1.55054	−	6.79337i	0.254907	−	1.11682i	−0.671709	−	0.740815i	$-0.734440\pi$
$37$	1.55054	−	6.79337i	0.254907	−	1.11682i	0.926617	−	0.376007i	$-0.122703\pi$
$38$	−0.0221769	+	0.0278090i	−0.00359757	+	0.00451121i
$39$		0			0
$40$	0.0383648	−	0.0305949i	0.00606601	−	0.00483748i
$41$	9.97587	+	4.80413i	1.55797	+	0.750278i	0.996988	−	0.0775505i	$-0.0247099\pi$
$41$	9.97587	+	4.80413i	1.55797	+	0.750278i	0.560981	+	0.827829i	$0.310424\pi$
$42$		0			0
$43$	0.0684189	−	0.0329488i	0.0104338	−	0.00502465i	−0.428660	−	0.903466i	$-0.641014\pi$
$43$	0.0684189	−	0.0329488i	0.0104338	−	0.00502465i	0.439093	+	0.898441i	$0.355300\pi$
$44$	−1.73302	+	3.59865i	−0.261262	+	0.542517i
$45$		0			0
$46$	0.0415164	+	0.0199932i	0.00612125	+	0.00294784i
$47$	3.46380	−	4.34347i	0.505247	−	0.633559i	−0.462157	−	0.886798i	$-0.652924\pi$
$47$	3.46380	−	4.34347i	0.505247	−	0.633559i	0.967404	+	0.253239i	$0.0814958\pi$
$48$		0			0
$49$	6.03450	+	3.54750i	0.862072	+	0.506786i
$50$			0.00153314i			0.000216818i
$51$		0			0
$52$	−1.22949	+	2.55306i	−0.170499	+	0.354045i
$53$	0.739555	−	0.168799i	0.101586	−	0.0231863i	−0.171426	−	0.985197i	$-0.554837\pi$
$53$	0.739555	−	0.168799i	0.101586	−	0.0231863i	0.273012	+	0.962011i	$0.411980\pi$
$54$		0			0
$55$	1.88422	+	3.91261i	0.254068	+	0.527577i
$56$	−0.0391230	+	0.0451023i	−0.00522802	+	0.00602705i
$57$		0			0
$58$	0.0197491	+	0.0247646i	0.00259318	+	0.00325175i
$59$	9.30068	−	4.47897i	1.21084	−	0.583112i	0.284097	−	0.958796i	$-0.408306\pi$
$59$	9.30068	−	4.47897i	1.21084	−	0.583112i	0.926748	+	0.375683i	$0.122592\pi$
$60$		0			0
$61$	7.51004	+	1.71412i	0.961562	+	0.219470i	0.674362	−	0.738401i	$-0.264419\pi$
$61$	7.51004	+	1.71412i	0.961562	+	0.219470i	0.287199	+	0.957871i	$0.407276\pi$
$62$	0.0183315	−	0.0229870i	0.00232810	−	0.00291935i
$63$		0			0
$64$	4.98744	+	6.25405i	0.623430	+	0.781757i
$65$	1.33675	+	2.77580i	0.165804	+	0.344295i
$66$		0			0
$67$	−8.97651			−1.09666			−0.548328	−	0.836263i	$-0.684735\pi$
$67$	−8.97651			−1.09666			−0.548328	+	0.836263i	$0.684735\pi$
$68$	−6.75700			−0.819406
$69$		0			0
$70$	0.00590892	+	0.0319149i	0.000706251	+	0.00381456i
$71$	14.3180	−	3.26798i	1.69923	−	0.387838i	0.740478	−	0.672080i	$-0.234599\pi$
$71$	14.3180	−	3.26798i	1.69923	−	0.387838i	0.958753	+	0.284242i	$0.0917419\pi$
$72$		0			0
$73$	2.21540	−	1.76672i	0.259293	−	0.206779i	−0.485211	−	0.874397i	$-0.661257\pi$
$73$	2.21540	−	1.76672i	0.259293	−	0.206779i	0.744504	+	0.667618i	$0.232686\pi$
$74$	−0.0307354	+	0.0245107i	−0.00357292	+	0.00284931i
$75$		0			0
$76$	−12.2929	+	2.80577i	−1.41009	+	0.321844i
$77$	−3.12098	−	4.26371i	−0.355668	−	0.485895i
$78$		0			0
$79$	−5.29436			−0.595662			−0.297831	−	0.954619i	$-0.596263\pi$
$79$	−5.29436			−0.595662			−0.297831	+	0.954619i	$0.596263\pi$
$80$	8.69740			0.972399
$81$		0			0
$82$	−0.0271036	−	0.0562813i	−0.00299310	−	0.00621523i
$83$	1.21293	+	1.52097i	0.133136	+	0.166948i	0.843931	−	0.536452i	$-0.180236\pi$
$83$	1.21293	+	1.52097i	0.133136	+	0.166948i	−0.710794	+	0.703400i	$0.751664\pi$
$84$		0			0
$85$	−4.58047	+	5.74373i	−0.496822	+	0.622995i
$86$	−0.000417688	0	9.53346e-5i	−4.50405e−5	0	1.02802e-5i
$87$		0			0
$88$	0.0406057	−	0.0195547i	0.00432858	−	0.00208453i
$89$	−4.85674	−	6.09016i	−0.514814	−	0.645556i	0.454685	−	0.890652i	$-0.349752\pi$
$89$	−4.85674	−	6.09016i	−0.514814	−	0.645556i	−0.969499	+	0.245096i	$0.921180\pi$
$90$		0			0
$91$	−2.21417	−	3.02489i	−0.232108	−	0.317094i
$92$	7.08749	+	14.7173i	0.738922	+	1.53439i
$93$		0			0
$94$	−0.0305569	+	0.00697441i	−0.00315170	+	0.000719355i
$95$	−5.94815	+	12.3515i	−0.610267	+	1.26723i
$96$		0			0
$97$			0.0843849i			0.00856799i	0.999991	+	0.00428399i	$0.00136364\pi$
$97$			0.0843849i			0.00856799i	−0.999991	+	0.00428399i	$0.998636\pi$
$98$	−0.0141390	−	0.0368744i	−0.00142825	−	0.00372488i
$99$		0			0
$100$	−0.338860	+	0.424917i	−0.0338860	+	0.0424917i
$101$	−5.10630	−	2.45906i	−0.508096	−	0.244686i	0.162230	−	0.986753i	$-0.448131\pi$
$101$	−5.10630	−	2.45906i	−0.508096	−	0.244686i	−0.670326	+	0.742067i	$0.733846\pi$
$102$		0			0
$103$	−3.75711	+	7.80172i	−0.370199	+	0.768726i	−0.999968	−	0.00805686i	$-0.997435\pi$
$103$	−3.75711	+	7.80172i	−0.370199	+	0.768726i	0.629769	+	0.776783i	$0.283150\pi$
$104$	0.0288076	−	0.0138730i	0.00282482	−	0.00136036i
$105$		0			0
$106$	−0.00385586	−	0.00185688i	−0.000374514	−	0.000180357i
$107$	−0.719156	+	0.573508i	−0.0695234	+	0.0554431i	−0.657635	−	0.753337i	$-0.728443\pi$
$107$	−0.719156	+	0.573508i	−0.0695234	+	0.0554431i	0.588111	+	0.808780i	$0.299872\pi$
$108$		0			0
$109$	0.286342	−	0.359062i	0.0274266	−	0.0343919i	−0.767929	−	0.640535i	$-0.778713\pi$
$109$	0.286342	−	0.359062i	0.0274266	−	0.0343919i	0.795356	+	0.606143i	$0.207284\pi$
$110$	0.00545182	−	0.0238860i	0.000519810	−	0.00227744i
$111$		0			0
$112$	−10.4057	+	1.92657i	−0.983242	+	0.182043i
$113$	10.8556	−	8.65707i	1.02121	−	0.814389i	0.0384487	−	0.999261i	$-0.487758\pi$
$113$	10.8556	−	8.65707i	1.02121	−	0.814389i	0.982763	+	0.184872i	$0.0591869\pi$
$114$		0			0
$115$	17.3149	+	3.95200i	1.61462	+	0.368526i
$116$			11.2286i			1.04255i
$117$		0			0
$118$	−0.0567794	−	0.0129595i	−0.00522697	−	0.00119302i
$119$	4.20782	−	7.88648i	0.385731	−	0.722952i
$120$		0			0
$121$	−1.56020	−	6.83567i	−0.141836	−	0.621425i
$122$	−0.0270964	−	0.0339779i	−0.00245320	−	0.00307621i
$123$		0			0
$124$	10.1613	−	2.31926i	0.912516	−	0.208276i
$125$	2.55080	+	11.1758i	0.228150	+	0.999591i
$126$		0			0
$127$	−1.48826	+	6.52048i	−0.132061	+	0.578599i	0.864985	+	0.501798i	$0.167328\pi$
$127$	−1.48826	+	6.52048i	−0.132061	+	0.578599i	−0.997046	+	0.0768013i	$0.975529\pi$
$128$		−	0.180529i		−	0.0159566i
$129$		0			0
$130$	0.00386778	−	0.0169459i	0.000339227	−	0.00148625i
$131$	17.0656	−	8.21835i	1.49103	−	0.718040i	0.501875	−	0.864940i	$-0.332644\pi$
$131$	17.0656	−	8.21835i	1.49103	−	0.718040i	0.989151	+	0.146900i	$0.0469295\pi$
$132$		0			0
$133$	4.38044	−	16.0950i	0.379833	−	1.39561i
$134$	0.0395944	+	0.0315755i	0.00342044	+	0.00272771i
$135$		0			0
$136$	0.0596093	+	0.0475368i	0.00511145	+	0.00407625i
$137$	7.35687	+	15.2767i	0.628540	+	1.30518i	0.935457	+	0.353440i	$0.114988\pi$
$137$	7.35687	+	15.2767i	0.628540	+	1.30518i	−0.306918	+	0.951736i	$0.599298\pi$
$138$		0			0
$139$	−6.52132	+	13.5417i	−0.553131	+	1.14859i	0.417647	+	0.908609i	$0.362855\pi$
$139$	−6.52132	+	13.5417i	−0.553131	+	1.14859i	−0.970778	+	0.239979i	$0.922859\pi$
$140$	−5.41627	+	10.1514i	−0.457758	+	0.857950i
$141$		0			0
$142$	−0.0746504	−	0.0359497i	−0.00626452	−	0.00301684i
$143$	0.629659	+	2.75872i	0.0526547	+	0.230696i
$144$		0			0
$145$	9.54481	+	7.61173i	0.792654	+	0.632120i
$146$	−0.0159864			−0.00132305
$147$		0			0
$148$	−13.9359			−1.14553
$149$	−7.96334	−	6.35056i	−0.652383	−	0.520258i	0.240441	−	0.970664i	$-0.422708\pi$
$149$	−7.96334	−	6.35056i	−0.652383	−	0.520258i	−0.892824	+	0.450406i	$0.851279\pi$
$150$		0			0
$151$	1.86646	+	8.17748i	0.151890	+	0.665474i	0.992335	+	0.123577i	$0.0394366\pi$
$151$	1.86646	+	8.17748i	0.151890	+	0.665474i	−0.840445	+	0.541897i	$0.817706\pi$
$152$	0.128185	+	0.0617307i	0.0103972	+	0.00500702i
$153$		0			0
$154$	−0.00123161	+	0.0297850i	−9.92463e−5	+	0.00240015i
$155$	4.91676	−	10.2098i	0.394924	−	0.820068i
$156$		0			0
$157$	1.92513	+	3.99758i	0.153642	+	0.319041i	0.963556	−	0.267508i	$-0.0862002\pi$
$157$	1.92513	+	3.99758i	0.153642	+	0.319041i	−0.809913	+	0.586550i	$0.800486\pi$
$158$	0.0233528	+	0.0186233i	0.00185785	+	0.00148159i
$159$		0			0
$160$	−0.115093	−	0.0917836i	−0.00909890	−	0.00725613i
$161$	−21.5911	−	0.892792i	−1.70162	−	0.0703619i
$162$		0			0
$163$	19.5157	−	9.39829i	1.52859	−	0.736131i	0.534550	−	0.845137i	$-0.320481\pi$
$163$	19.5157	−	9.39829i	1.52859	−	0.736131i	0.994041	+	0.109006i	$0.0347669\pi$
$164$	4.92759	−	21.5892i	0.384780	−	1.68583i
$165$		0			0
$166$		−	0.0109754i		−	0.000851855i
$167$	2.41521	−	10.5817i	0.186895	−	0.818839i	−0.791347	−	0.611368i	$-0.790620\pi$
$167$	2.41521	−	10.5817i	0.186895	−	0.818839i	0.978241	−	0.207471i	$-0.0665233\pi$
$168$		0			0
$169$	−2.44606	−	10.7169i	−0.188159	−	0.824377i
$170$	0.0404079	−	0.00922285i	0.00309915	−	0.000707360i
$171$		0			0
$172$	−0.0946932	−	0.118742i	−0.00722029	−	0.00905396i
$173$	−4.19091	−	18.3616i	−0.318629	−	1.39600i	−0.839960	−	0.542649i	$-0.817421\pi$
$173$	−4.19091	−	18.3616i	−0.318629	−	1.39600i	0.521331	−	0.853355i	$-0.325436\pi$
$174$		0			0
$175$	−0.284925	−	0.660114i	−0.0215383	−	0.0498999i
$176$	7.78787	+	1.77753i	0.587033	+	0.133986i
$177$		0			0
$178$			0.0439470i			0.00329397i
$179$	−7.92157	−	1.80805i	−0.592086	−	0.135140i	−0.0840291	−	0.996463i	$-0.526779\pi$
$179$	−7.92157	−	1.80805i	−0.592086	−	0.135140i	−0.508057	+	0.861324i	$0.669636\pi$
$180$		0			0
$181$	0.621193	−	0.495385i	0.0461729	−	0.0368217i	−0.600131	−	0.799901i	$-0.704885\pi$
$181$	0.621193	−	0.495385i	0.0461729	−	0.0368217i	0.646304	+	0.763080i	$0.276314\pi$
$182$	−0.000873767		0.0211310i	−6.47679e−5		0.00156633i
$183$		0			0
$184$	0.0410145	−	0.179696i	0.00302363	−	0.0132474i
$185$	−9.44696	+	11.8461i	−0.694554	+	0.870944i
$186$		0			0
$187$	−5.27534	+	4.20695i	−0.385771	+	0.307642i
$188$	−10.0105	−	4.82081i	−0.730091	−	0.351593i
$189$		0			0
$190$	0.0696837	−	0.0335579i	0.00505539	−	0.00243455i
$191$	−2.97564	+	6.17897i	−0.215310	+	0.447095i	−0.980450	−	0.196769i	$-0.936955\pi$
$191$	−2.97564	+	6.17897i	−0.215310	+	0.447095i	0.765140	+	0.643863i	$0.222670\pi$
$192$		0			0
$193$	−21.8437	−	10.5194i	−1.57234	−	0.757200i	−0.574234	−	0.818691i	$-0.694700\pi$
$193$	−21.8437	−	10.5194i	−1.57234	−	0.757200i	−0.998108	+	0.0614911i	$0.980414\pi$
$194$	0.000296830	0	0.000372213i	2.13111e−5	0	2.67233e-5i
$195$		0			0
$196$	4.23144	−	13.3450i	0.302246	−	0.953213i
$197$			13.1835i			0.939284i	0.882857	+	0.469642i	$0.155617\pi$
$197$			13.1835i			0.939284i	−0.882857	+	0.469642i	$0.844383\pi$
$198$		0			0
$199$	5.36518	−	11.1409i	0.380328	−	0.789759i	−0.619660	−	0.784870i	$-0.712730\pi$
$199$	5.36518	−	11.1409i	0.380328	−	0.789759i	0.999988	−	0.00488858i	$-0.00155609\pi$
$200$	0.00597875	−	0.00136461i	0.000422761	−	9.64925e-5i
$201$		0			0
$202$	0.0138734	+	0.0288084i	0.000976130	+	0.00202695i
$203$	−13.1056	−	6.99248i	−0.919832	−	0.490776i
$204$		0			0
$205$	−15.0114	−	18.8237i	−1.04844	−	1.31470i
$206$	0.0440153	−	0.0211966i	0.00306669	−	0.00147684i
$207$		0			0
$208$	5.52509	+	1.26107i	0.383096	+	0.0874392i
$209$	−7.85045	+	9.84415i	−0.543027	+	0.680934i
$210$		0			0
$211$	12.6490	+	15.8613i	0.870793	+	1.09194i	0.995019	+	0.0996861i	$0.0317839\pi$
$211$	12.6490	+	15.8613i	0.870793	+	1.09194i	−0.124226	+	0.992254i	$0.539645\pi$
$212$	−0.658256	−	1.36688i	−0.0452092	−	0.0938778i
$213$		0			0
$214$	0.00518947			0.000354745
$215$	−0.165126			−0.0112615
$216$		0			0
$217$	−3.62089	+	13.3042i	−0.245802	+	0.903146i
$218$	−0.00252605		0.000576554i	−0.000171086		3.90492e-5i
$219$		0			0
$220$	6.79037	−	5.41514i	0.457807	−	0.365089i
$221$	−3.74258	+	2.98461i	−0.251753	+	0.200767i
$222$		0			0
$223$	9.56540	−	2.18324i	0.640547	−	0.146201i	0.110102	−	0.993920i	$-0.464882\pi$
$223$	9.56540	−	2.18324i	0.640547	−	0.146201i	0.530444	+	0.847720i	$0.322025\pi$
$224$	0.158029	+	0.0843165i	0.0105588	+	0.00563363i
$225$		0			0
$226$	−0.0783349			−0.00521076
$227$	0.229766			0.0152501			0.00762505	−	0.999971i	$-0.497573\pi$
$227$	0.229766			0.0152501			0.00762505	+	0.999971i	$0.497573\pi$
$228$		0			0
$229$	−5.92639	−	12.3063i	−0.391627	−	0.813222i	−0.999811	−	0.0194260i	$-0.993816\pi$
$229$	−5.92639	−	12.3063i	−0.391627	−	0.813222i	0.608184	−	0.793796i	$-0.291898\pi$
$230$	−0.0624725	−	0.0783381i	−0.00411932	−	0.00516546i
$231$		0			0
$232$	0.0789957	−	0.0990574i	0.00518632	−	0.00650344i
$233$	−17.3937	−	3.96999i	−1.13950	−	0.260083i	−0.389180	−	0.921162i	$-0.627242\pi$
$233$	−17.3937	−	3.96999i	−1.13950	−	0.260083i	−0.750316	+	0.661079i	$0.770099\pi$
$234$		0			0
$235$	−10.8839	+	5.24139i	−0.709985	+	0.341911i
$236$	−12.8723	−	16.1414i	−0.837917	−	1.05072i
$237$		0			0
$238$	−0.0463015	+	0.0199851i	−0.00300128	+	0.00129544i
$239$	4.82970	+	10.0290i	0.312408	+	0.648721i	0.996760	−	0.0804301i	$-0.0256294\pi$
$239$	4.82970	+	10.0290i	0.312408	+	0.648721i	−0.684353	+	0.729151i	$0.739915\pi$
$240$		0			0
$241$	−16.8259	+	3.84041i	−1.08385	+	0.247382i	−0.726902	−	0.686741i	$-0.759041\pi$
$241$	−16.8259	+	3.84041i	−1.08385	+	0.247382i	−0.356951	+	0.934123i	$0.616184\pi$
$242$	−0.0171631	+	0.0356395i	−0.00110328	+	0.00229099i
$243$		0			0
$244$		−	15.4061i		−	0.986274i
$245$	−8.47537	−	12.6433i	−0.541471	−	0.807749i
$246$		0			0
$247$	−5.56949	+	6.98392i	−0.354378	+	0.444376i
$248$	−0.105958	−	0.0510269i	−0.00672836	−	0.00324021i
$249$		0			0
$250$	0.0280603	−	0.0582677i	0.00177469	−	0.00368517i
$251$	16.8505	−	8.11476i	1.06359	−	0.512199i	0.181556	−	0.983381i	$-0.441887\pi$
$251$	16.8505	−	8.11476i	1.06359	−	0.512199i	0.882036	+	0.471181i	$0.156172\pi$
$252$		0			0
$253$	14.6965	+	7.07744i	0.923959	+	0.444955i
$254$	0.0295008	−	0.0235261i	0.00185104	−	0.00147616i
$255$		0			0
$256$	9.97425	−	12.5073i	0.623391	−	0.781707i
$257$	−6.48011	+	28.3912i	−0.404218	+	1.77099i	0.205787	+	0.978597i	$0.434024\pi$
$257$	−6.48011	+	28.3912i	−0.404218	+	1.77099i	−0.610005	+	0.792397i	$0.708833\pi$
$258$		0			0
$259$	8.67840	−	16.2654i	0.539249	−	1.01068i
$260$	4.81742	−	3.84176i	0.298764	−	0.238256i
$261$		0			0
$262$	−0.104183	−	0.0237791i	−0.00643645	−	0.00146908i
$263$			26.8737i			1.65710i	0.559912	+	0.828552i	$0.310835\pi$
$263$			26.8737i			1.65710i	−0.559912	+	0.828552i	$0.689165\pi$
$264$		0			0
$265$	−1.60813	−	0.367045i	−0.0987866	−	0.0225474i
$266$	−0.0759369	+	0.0555847i	−0.00465599	+	0.00340812i
$267$		0			0
$268$	3.99486	+	17.5026i	0.244025	+	1.06914i
$269$	−2.49263	−	3.12566i	−0.151979	−	0.190575i	0.700014	−	0.714129i	$-0.253177\pi$
$269$	−2.49263	−	3.12566i	−0.151979	−	0.190575i	−0.851992	+	0.523554i	$0.824606\pi$
$270$		0			0
$271$	25.7952	−	5.88759i	1.56695	−	0.357646i	0.651043	−	0.759041i	$-0.274332\pi$
$271$	25.7952	−	5.88759i	1.56695	−	0.357646i	0.915905	+	0.401395i	$0.131475\pi$
$272$	3.00705	+	13.1748i	0.182329	+	0.798837i
$273$		0			0
$274$	0.0212865	−	0.0932621i	0.00128596	−	0.00563417i
$275$			0.542719i			0.0327272i
$276$		0			0
$277$	2.05960	−	9.02368i	0.123749	−	0.542180i	−0.874605	−	0.484836i	$-0.838879\pi$
$277$	2.05960	−	9.02368i	0.123749	−	0.542180i	0.998354	−	0.0573448i	$-0.0182634\pi$
$278$	0.0763985	−	0.0367916i	0.00458208	−	0.00220661i
$279$		0			0
$280$	0.119199	−	0.0514496i	0.00712348	−	0.00307470i
$281$	−12.0953	−	9.64571i	−0.721547	−	0.575415i	0.192367	−	0.981323i	$-0.438384\pi$
$281$	−12.0953	−	9.64571i	−0.721547	−	0.575415i	−0.913914	+	0.405908i	$0.866955\pi$
$282$		0			0
$283$	−10.6669	−	8.50654i	−0.634079	−	0.505661i	0.252887	−	0.967496i	$-0.418620\pi$
$283$	−10.6669	−	8.50654i	−0.634079	−	0.505661i	−0.886966	+	0.461835i	$0.847191\pi$
$284$	−12.7440	−	26.4632i	−0.756217	−	1.57030i
$285$		0			0
$286$	0.00692662	−	0.0143833i	0.000409580	−	0.000850501i
$287$	22.1294	+	19.1956i	1.30626	+	1.13308i
$288$		0			0
$289$	5.03226	+	2.42341i	0.296015	+	0.142553i
$290$	−0.0153263	−	0.0671491i	−0.000899994	−	0.00394313i
$291$		0			0
$292$	−4.43073	−	3.53339i	−0.259289	−	0.206776i
$293$	−2.88801			−0.168720			−0.0843598	−	0.996435i	$-0.526885\pi$
$293$	−2.88801			−0.168720			−0.0843598	+	0.996435i	$0.526885\pi$
$294$		0			0
$295$	−22.4468			−1.30691
$296$	0.122941	+	0.0980419i	0.00714578	+	0.00569857i
$297$		0			0
$298$	0.0127869	+	0.0560232i	0.000740727	+	0.00324534i
$299$	10.4264	+	5.02108i	0.602973	+	0.290377i
$300$		0			0
$301$	0.197559	−	0.0365772i	0.0113871	−	0.00210828i
$302$	0.0205321	−	0.0426354i	0.00118149	−	0.00245339i
$303$		0			0
$304$	10.9413	+	22.7199i	0.627529	+	1.30308i
$305$	−13.0958	−	10.4436i	−0.749865	−	0.597997i
$306$		0			0
$307$	−13.0948	−	10.4428i	−0.747361	−	0.596001i	0.173983	−	0.984749i	$-0.444336\pi$
$307$	−13.0948	−	10.4428i	−0.747361	−	0.596001i	−0.921344	+	0.388748i	$0.872908\pi$
$308$	−6.92455	+	7.98286i	−0.394563	+	0.454866i
$309$		0			0
$310$	−0.0576009	+	0.0277391i	−0.00327151	+	0.00157548i
$311$	4.95676	−	21.7170i	0.281072	−	1.23146i	−0.615349	−	0.788254i	$-0.710985\pi$
$311$	4.95676	−	21.7170i	0.281072	−	1.23146i	0.896421	−	0.443203i	$-0.146158\pi$
$312$		0			0
$313$		−	11.6294i		−	0.657335i	−0.944446	−	0.328667i	$-0.893400\pi$
$313$		−	11.6294i		−	0.657335i	0.944446	−	0.328667i	$-0.106600\pi$
$314$	0.00557021	−	0.0244047i	0.000314345	−	0.00137724i
$315$		0			0
$316$	2.35617	+	10.3231i	0.132545	+	0.580718i
$317$	−3.39782	+	0.775530i	−0.190841	+	0.0435581i	−0.316873	−	0.948468i	$-0.602633\pi$
$317$	−3.39782	+	0.775530i	−0.190841	+	0.0435581i	0.126032	+	0.992026i	$0.459776\pi$
$318$		0			0
$319$	6.99102	+	8.76646i	0.391422	+	0.490827i
$320$	−3.87052	−	16.9579i	−0.216369	−	0.947974i
$321$		0			0
$322$	0.0920955	+	0.0798861i	0.00513228	+	0.00445188i
$323$	−20.7664	−	4.73980i	−1.15547	−	0.263729i
$324$		0			0
$325$			0.385031i			0.0213577i
$326$	−0.119141	−	0.0271931i	−0.00659861	−	0.00150609i
$327$		0			0
$328$	−0.195355	+	0.155790i	−0.0107867	+	0.00860208i
$329$	11.8605	−	8.68174i	0.653893	−	0.478640i
$330$		0			0
$331$	−0.637151	+	2.79154i	−0.0350210	+	0.153437i	−0.989415	−	0.145112i	$-0.953646\pi$
$331$	−0.637151	+	2.79154i	−0.0350210	+	0.153437i	0.954394	+	0.298549i	$0.0965028\pi$
$332$	2.42582	−	3.04188i	0.133134	−	0.166945i
$333$		0			0
$334$	−0.0478752	+	0.0381792i	−0.00261962	+	0.00208907i
$335$	17.5860	+	8.46898i	0.960827	+	0.462710i
$336$		0			0
$337$	12.0356	−	5.79603i	0.655620	−	0.315730i	−0.0763357	−	0.997082i	$-0.524322\pi$
$337$	12.0356	−	5.79603i	0.655620	−	0.315730i	0.731956	+	0.681352i	$0.238608\pi$
$338$	−0.0269081	+	0.0558753i	−0.00146361	+	0.00303921i
$339$		0			0
$340$	13.2377	+	6.37496i	0.717917	+	0.345731i
$341$	6.48921	−	8.13721i	0.351410	−	0.440655i
$342$		0			0
$343$	12.9406	+	13.2492i	0.698728	+	0.715387i
$344$			0.00171371i			9.23968e-5i
$345$		0			0
$346$	−0.0461024	+	0.0957327i	−0.00247848	+	0.00514662i
$347$	28.8400	−	6.58255i	1.54821	−	0.353370i	0.638837	−	0.769342i	$-0.279416\pi$
$347$	28.8400	−	6.58255i	1.54821	−	0.353370i	0.909377	+	0.415973i	$0.136559\pi$
$348$		0			0
$349$	3.66406	+	7.60850i	0.196133	+	0.407273i	0.975721	−	0.219019i	$-0.0702858\pi$
$349$	3.66406	+	7.60850i	0.196133	+	0.407273i	−0.779588	+	0.626293i	$0.784571\pi$
$350$	−0.00106522	+	0.00391393i	−5.69386e−5	+	0.000209209i
$351$		0			0
$352$	−0.0842988	−	0.105707i	−0.00449314	−	0.00563422i
$353$	3.11324	−	1.49926i	0.165701	−	0.0797975i	−0.349195	−	0.937050i	$-0.613545\pi$
$353$	3.11324	−	1.49926i	0.165701	−	0.0797975i	0.514896	+	0.857253i	$0.327831\pi$
$354$		0			0
$355$	−31.1338	−	7.10608i	−1.65241	−	0.377152i
$356$	−9.71333	+	12.1801i	−0.514805	+	0.645546i
$357$		0			0
$358$	0.0285813	+	0.0358398i	0.00151057	+	0.00189419i
$359$	0.761364	+	1.58099i	0.0401832	+	0.0834414i	0.920094	−	0.391698i	$-0.128112\pi$
$359$	0.761364	+	1.58099i	0.0401832	+	0.0834414i	−0.879911	+	0.475139i	$0.842398\pi$
$360$		0			0
$361$	−20.7481			−1.09200
$362$	−0.00448257			−0.000235599
$363$		0			0
$364$	−4.91261	+	5.66343i	−0.257491	+	0.296844i
$365$	−6.00705	+	1.37107i	−0.314423	+	0.0717651i
$366$		0			0
$367$	−18.1667	+	14.4874i	−0.948292	+	0.756237i	−0.969894	−	0.243529i	$-0.921695\pi$
$367$	−18.1667	+	14.4874i	−0.948292	+	0.756237i	0.0216020	+	0.999767i	$0.493123\pi$
$368$	25.5416	−	20.3688i	1.33145	−	1.06180i
$369$		0			0
$370$	0.0833390	−	0.0190216i	0.00433259	−	0.000988886i
$371$	2.00529	+	0.0829187i	0.104109	+	0.00430492i
$372$		0			0
$373$	−11.8862			−0.615444			−0.307722	−	0.951476i	$-0.599567\pi$
$373$	−11.8862			−0.615444			−0.307722	+	0.951476i	$0.599567\pi$
$374$	0.0380672			0.00196841
$375$		0			0
$376$	0.0543959	+	0.112954i	0.00280526	+	0.00582517i
$377$	4.95977	+	6.21935i	0.255441	+	0.320313i
$378$		0			0
$379$	5.68424	−	7.12782i	0.291980	−	0.366131i	−0.614107	−	0.789223i	$-0.710484\pi$
$379$	5.68424	−	7.12782i	0.291980	−	0.366131i	0.906087	+	0.423091i	$0.139055\pi$
$380$	26.7303	+	6.10102i	1.37124	+	0.312976i
$381$		0			0
$382$	0.0348602	−	0.0167878i	0.00178360	−	0.000858938i
$383$	17.3778	+	21.7911i	0.887967	+	1.11347i	0.992895	+	0.118995i	$0.0379672\pi$
$383$	17.3778	+	21.7911i	0.887967	+	1.11347i	−0.104928	+	0.994480i	$0.533461\pi$
$384$		0			0
$385$	2.09171	+	11.2976i	0.106603	+	0.575780i
$386$	0.0593475	+	0.123236i	0.00302071	+	0.00627257i
$387$		0			0
$388$	0.164536	−	0.0375542i	0.00835304	−	0.00190653i
$389$	−0.260129	+	0.540163i	−0.0131891	+	0.0273873i	−0.907459	−	0.420140i	$-0.861981\pi$
$389$	−0.260129	+	0.540163i	−0.0131891	+	0.0273873i	0.894270	+	0.447527i	$0.147695\pi$
$390$		0			0
$391$			27.5948i			1.39553i
$392$	−0.131214	+	0.0879586i	−0.00662729	+	0.00444258i
$393$		0			0
$394$	0.0463738	−	0.0581509i	0.00233628	−	0.00292960i
$395$	10.3723	+	4.99502i	0.521885	+	0.251327i
$396$		0			0
$397$	−11.9753	+	24.8669i	−0.601021	+	1.24803i	0.349373	+	0.936984i	$0.386395\pi$
$397$	−11.9753	+	24.8669i	−0.601021	+	1.24803i	−0.950394	+	0.311049i	$0.899320\pi$
$398$	−0.0628542	+	0.0302690i	−0.00315060	+	0.00151725i
$399$		0			0
$400$	0.979302	+	0.471607i	0.0489651	+	0.0235804i
$401$	−19.0713	+	15.2089i	−0.952376	+	0.759495i	−0.970689	−	0.240338i	$-0.922742\pi$
$401$	−19.0713	+	15.2089i	−0.952376	+	0.759495i	0.0183131	+	0.999832i	$0.494170\pi$
$402$		0			0
$403$	4.60376	−	5.77293i	0.229330	−	0.287570i
$404$	−2.52226	+	11.0508i	−0.125487	+	0.549796i
$405$		0			0
$406$	0.0332108	+	0.0769429i	0.00164822	+	0.00381861i
$407$	−10.8801	+	8.67658i	−0.539306	+	0.430082i
$408$		0			0
$409$	9.36470	+	2.13743i	0.463055	+	0.105689i	0.447682	−	0.894193i	$-0.352250\pi$
$409$	9.36470	+	2.13743i	0.463055	+	0.105689i	0.0153722	+	0.999882i	$0.495107\pi$
$410$			0.135833i			0.00670830i
$411$		0			0
$412$	16.8840	+	3.85367i	0.831816	+	0.189857i
$413$	26.8556	−	4.97221i	1.32148	−	0.244666i
$414$		0			0
$415$	−0.941299	−	4.12410i	−0.0462065	−	0.202444i
$416$	−0.0598057	−	0.0749940i	−0.00293222	−	0.00367688i
$417$		0			0
$418$	0.0692550	−	0.0158070i	0.00338737	−	0.000773145i
$419$	−2.86994	−	12.5740i	−0.140206	−	0.614282i	−0.995386	−	0.0959514i	$-0.969411\pi$
$419$	−2.86994	−	12.5740i	−0.140206	−	0.614282i	0.855180	−	0.518331i	$-0.173446\pi$
$420$		0			0
$421$	6.87283	−	30.1118i	0.334961	−	1.46756i	−0.474431	−	0.880293i	$-0.657346\pi$
$421$	6.87283	−	30.1118i	0.334961	−	1.46756i	0.809392	−	0.587268i	$-0.199797\pi$
$422$		−	0.114456i		−	0.00557165i
$423$		0			0
$424$	−0.00380924	+	0.0166894i	−0.000184993	+	0.000810508i
$425$	−0.827196	+	0.398356i	−0.0401249	+	0.0193231i
$426$		0			0
$427$	17.9813	+	9.59393i	0.870178	+	0.464283i
$428$	1.43829	+	1.14700i	0.0695223	+	0.0554422i
$429$		0			0
$430$	0.000728355	0	0.000580844i	3.51244e−5	0	2.80108e-5i
$431$	2.74151	+	5.69280i	0.132054	+	0.274213i	0.956503	−	0.291724i	$-0.0942289\pi$
$431$	2.74151	+	5.69280i	0.132054	+	0.274213i	−0.824449	+	0.565937i	$0.808515\pi$
$432$		0			0
$433$	3.96743	−	8.23846i	0.190663	−	0.395915i	−0.783621	−	0.621239i	$-0.786630\pi$
$433$	3.96743	−	8.23846i	0.190663	−	0.395915i	0.974284	+	0.225324i	$0.0723440\pi$
$434$	0.0627697	−	0.0459465i	0.00301304	−	0.00220550i
$435$		0			0
$436$	−0.827539	−	0.398522i	−0.0396319	−	0.0190857i
$437$	11.4584	+	50.2027i	0.548131	+	2.40152i
$438$		0			0
$439$	2.36090	+	1.88276i	0.112680	+	0.0898590i	0.678209	−	0.734869i	$-0.262757\pi$
$439$	2.36090	+	1.88276i	0.112680	+	0.0898590i	−0.565529	+	0.824728i	$0.691328\pi$
$440$	−0.0980002			−0.00467198
$441$		0			0
$442$	0.0270067			0.00128458
$443$	4.28966	+	3.42089i	0.203808	+	0.162531i	0.720075	−	0.693896i	$-0.244107\pi$
$443$	4.28966	+	3.42089i	0.203808	+	0.162531i	−0.516267	+	0.856428i	$0.672679\pi$
$444$		0			0
$445$	3.76909	+	16.5135i	0.178672	+	0.782814i
$446$	−0.0498717	−	0.0240169i	−0.00236149	−	0.00113723i
$447$		0			0
$448$	8.38708	+	19.4312i	0.396252	+	0.918038i
$449$	1.88400	−	3.91217i	0.0889115	−	0.184627i	−0.851771	−	0.523914i	$-0.824471\pi$
$449$	1.88400	−	3.91217i	0.0889115	−	0.184627i	0.940683	+	0.339287i	$0.110186\pi$
$450$		0			0
$451$	−9.59448	−	19.9231i	−0.451786	−	0.938144i
$452$	−21.7109	−	17.3139i	−1.02120	−	0.814376i
$453$		0			0
$454$	−0.00101347		0.000808218i	−4.75646e−5		3.79315e-5i
$455$	1.48396	+	8.01509i	0.0695692	+	0.375753i
$456$		0			0
$457$	−28.7245	+	13.8330i	−1.34368	+	0.647080i	−0.960935	−	0.276776i	$-0.910734\pi$
$457$	−28.7245	+	13.8330i	−1.34368	+	0.647080i	−0.382741	+	0.923856i	$0.625020\pi$
$458$	−0.0171475	+	0.0751282i	−0.000801251	+	0.00351051i
$459$		0			0
$460$		−	35.5197i		−	1.65612i
$461$	0.764762	−	3.35064i	0.0356185	−	0.156055i	−0.953991	−	0.299835i	$-0.903069\pi$
$461$	0.764762	−	3.35064i	0.0356185	−	0.156055i	0.989610	+	0.143780i	$0.0459256\pi$
$462$		0			0
$463$	−2.98438	−	13.0754i	−0.138696	−	0.607667i	−0.995722	−	0.0923947i	$-0.970548\pi$
$463$	−2.98438	−	13.0754i	−0.138696	−	0.607667i	0.857026	−	0.515273i	$-0.172309\pi$
$464$	21.8935	−	4.99706i	1.01638	−	0.231982i
$465$		0			0
$466$	0.0627569	+	0.0786946i	0.00290716	+	0.00364546i
$467$	2.77375	+	12.1526i	0.128354	+	0.562356i	0.997678	+	0.0681125i	$0.0216977\pi$
$467$	2.77375	+	12.1526i	0.128354	+	0.562356i	−0.869324	+	0.494243i	$0.835445\pi$
$468$		0			0
$469$	−22.9161	−	6.23689i	−1.05817	−	0.287993i
$470$	0.0664445	+	0.0151655i	0.00306486	+	0.000699534i
$471$		0			0
$472$			0.232956i			0.0107227i
$473$	−0.147858	−	0.0337477i	−0.00679853	−	0.00155172i
$474$		0			0
$475$	−1.33949	+	1.06821i	−0.0614600	+	0.0490127i
$476$	−17.2499	−	4.69476i	−0.790647	−	0.215184i
$477$		0			0
$478$	0.0139743	−	0.0612256i	0.000639172	−	0.00280039i
$479$	−20.1015	+	25.2064i	−0.918460	+	1.15171i	0.0695899	+	0.997576i	$0.477831\pi$
$479$	−20.1015	+	25.2064i	−0.918460	+	1.15171i	−0.988050	+	0.154136i	$0.950740\pi$
$480$		0			0
$481$	−7.71886	+	6.15559i	−0.351950	+	0.280671i
$482$	0.0877262	+	0.0422467i	0.00399582	+	0.00192429i
$483$		0			0
$484$	−12.6340	+	6.08422i	−0.574273	+	0.276556i
$485$	0.0796138	−	0.165320i	0.00361508	−	0.00750678i
$486$		0			0
$487$	6.02530	+	2.90163i	0.273032	+	0.131485i	0.565390	−	0.824824i	$-0.308726\pi$
$487$	6.02530	+	2.90163i	0.273032	+	0.131485i	−0.292358	+	0.956309i	$0.594440\pi$
$488$	−0.108385	+	0.135910i	−0.00490635	+	0.00615237i
$489$		0			0
$490$	−0.00708967	+	0.0855808i	−0.000320279	+	0.00386615i
$491$		−	13.6184i		−	0.614588i	−0.951615	−	0.307294i	$-0.900577\pi$
$491$		−	13.6184i		−	0.614588i	0.951615	−	0.307294i	$-0.0994235\pi$
$492$		0			0
$493$	−8.23016	+	17.0901i	−0.370668	+	0.769699i
$494$	0.0491328	−	0.0112142i	0.00221059	−	0.000504553i
$495$		0			0
$496$	−9.04416	−	18.7804i	−0.406095	−	0.843264i
$497$	38.8228	+	1.60533i	1.74144	+	0.0720087i
$498$		0			0
$499$	26.4561	+	33.1748i	1.18434	+	1.48511i	0.836856	+	0.547422i	$0.184391\pi$
$499$	26.4561	+	33.1748i	1.18434	+	1.48511i	0.347479	+	0.937688i	$0.387038\pi$
$500$	20.6556	−	9.94721i	0.923747	−	0.444853i
$501$		0			0
$502$	−0.102870	−	0.0234794i	−0.00459131	−	0.00104794i
$503$	15.7566	−	19.7581i	0.702550	−	0.880970i	−0.294661	−	0.955602i	$-0.595207\pi$
$503$	15.7566	−	19.7581i	0.702550	−	0.880970i	0.997211	+	0.0746320i	$0.0237782\pi$
$504$		0			0
$505$	7.68380	+	9.63518i	0.341925	+	0.428760i
$506$	−0.0399291	−	0.0829137i	−0.00177507	−	0.00368596i
$507$		0			0
$508$	13.3761			0.593469
$509$	−44.4455			−1.97001			−0.985006	−	0.172523i	$-0.944808\pi$
$509$	−44.4455			−1.97001			−0.985006	+	0.172523i	$0.944808\pi$
$510$		0			0
$511$	6.88319	−	2.97099i	0.304494	−	0.131429i
$512$	−0.439995	+	0.100426i	−0.0194452	+	0.00443825i
$513$		0			0
$514$	0.128451	−	0.102436i	0.00566573	−	0.00451827i
$515$	14.7212	−	11.7398i	0.648694	−	0.517317i
$516$		0			0
$517$	−10.8169	+	2.46889i	−0.475726	+	0.108581i
$518$	−0.0954942	+	0.0412181i	−0.00419577	+	0.00181102i
$519$		0			0
$520$	−0.0695261			−0.00304892
$521$	−20.3446			−0.891314			−0.445657	−	0.895204i	$-0.647030\pi$
$521$	−20.3446			−0.891314			−0.445657	+	0.895204i	$0.647030\pi$
$522$		0			0
$523$	17.8019	+	36.9660i	0.778421	+	1.61641i	0.787395	+	0.616449i	$0.211429\pi$
$523$	17.8019	+	36.9660i	0.778421	+	1.61641i	−0.00897326	+	0.999960i	$0.502856\pi$
$524$	−23.6191	−	29.6174i	−1.03181	−	1.29384i
$525$		0			0
$526$	0.0945302	−	0.118537i	0.00412171	−	0.00516846i
$527$	17.1656	+	3.91793i	0.747745	+	0.170668i
$528$		0			0
$529$	39.3816	−	18.9652i	1.71224	−	0.824572i
$530$	0.00580218	+	0.00727570i	0.000252031	+	0.000316036i
$531$		0			0
$532$	−33.3318	−	1.37827i	−1.44512	−	0.0597557i
$533$	−6.80679	−	14.1344i	−0.294835	−	0.612231i
$534$		0			0
$535$	1.94999	−	0.445073i	0.0843055	−	0.0192422i
$536$	0.0878923	−	0.182510i	0.00379637	−	0.00788324i
$537$		0			0
$538$			0.0225550i			0.000972414i
$539$	−5.00509	−	13.0533i	−0.215584	−	0.562244i
$540$		0			0
$541$	11.8503	−	14.8599i	0.509486	−	0.638875i	−0.458854	−	0.888512i	$-0.651740\pi$
$541$	11.8503	−	14.8599i	0.509486	−	0.638875i	0.968340	+	0.249637i	$0.0803112\pi$
$542$	−0.134490	−	0.0647669i	−0.00577684	−	0.00278198i
$543$		0			0
$544$	0.0992406	−	0.206075i	0.00425491	−	0.00883540i
$545$	−0.899738	+	0.433291i	−0.0385405	+	0.0185601i
$546$		0			0
$547$	−29.3752	−	14.1463i	−1.25599	−	0.604853i	−0.316879	−	0.948466i	$-0.602635\pi$
$547$	−29.3752	−	14.1463i	−1.25599	−	0.604853i	−0.939111	+	0.343613i	$0.888349\pi$
$548$	26.5128	−	21.1433i	1.13257	−	0.903195i
$549$		0			0
$550$	0.00190905	−	0.00239387i	8.14022e−5	−	0.000102075i
$551$	−7.87650	+	34.5092i	−0.335550	+	1.47014i
$552$		0			0
$553$	−13.5159	−	3.67852i	−0.574755	−	0.156427i
$554$	−0.0408261	+	0.0325577i	−0.00173453	+	0.00138324i
$555$		0			0
$556$	29.3061	+	6.68892i	1.24285	+	0.283673i
$557$			7.44376i			0.315402i	0.987487	+	0.157701i	$0.0504082\pi$
$557$			7.44376i			0.315402i	−0.987487	+	0.157701i	$0.949592\pi$
$558$		0			0
$559$	−0.104898	−	0.0239423i	−0.00443671	−	0.00101265i
$560$	22.2035	+	6.04296i	0.938270	+	0.255362i
$561$		0			0
$562$	0.0194218	+	0.0850924i	0.000819258	+	0.00358940i
$563$	−16.5053	−	20.6970i	−0.695617	−	0.872276i	0.301071	−	0.953602i	$-0.402656\pi$
$563$	−16.5053	−	20.6970i	−0.695617	−	0.872276i	−0.996688	+	0.0813261i	$0.974084\pi$
$564$		0			0
$565$	−29.4350	+	6.71835i	−1.23834	+	0.282643i
$566$	0.0171280	+	0.0750428i	0.000719945	+	0.00315429i
$567$		0			0
$568$	−0.0737479	+	0.323111i	−0.00309439	+	0.0135574i
$569$		−	23.8408i		−	0.999457i	−0.866182	−	0.499729i	$-0.833433\pi$
$569$		−	23.8408i		−	0.999457i	0.866182	−	0.499729i	$-0.166567\pi$
$570$		0			0
$571$	3.87073	−	16.9588i	0.161985	−	0.709702i	−0.827063	−	0.562109i	$-0.809990\pi$
$571$	3.87073	−	16.9588i	0.161985	−	0.709702i	0.989048	−	0.147593i	$-0.0471526\pi$
$572$	5.09879	−	2.45545i	0.213191	−	0.102668i
$573$		0			0
$574$	−0.0300884	−	0.162512i	−0.00125586	−	0.00678310i
$575$	1.73531	+	1.38386i	0.0723674	+	0.0577111i
$576$		0			0
$577$	−36.5255	−	29.1281i	−1.52058	−	1.21262i	−0.905644	−	0.424038i	$-0.860612\pi$
$577$	−36.5255	−	29.1281i	−1.52058	−	1.21262i	−0.614931	−	0.788581i	$-0.710816\pi$
$578$	−0.0136722	−	0.0283907i	−0.000568690	−	0.00118090i
$579$		0			0
$580$	10.5938	−	21.9982i	0.439883	−	0.913426i
$581$	2.03971	+	4.72560i	0.0846214	+	0.196051i
$582$		0			0
$583$	−1.36494	−	0.657322i	−0.0565302	−	0.0272235i
$584$	0.0142292	+	0.0623420i	0.000588807	+	0.00257973i
$585$		0			0
$586$	0.0127387	+	0.0101588i	0.000526232	+	0.000419656i
$587$	−29.2649			−1.20789			−0.603946	−	0.797025i	$-0.706406\pi$
$587$	−29.2649			−1.20789			−0.603946	+	0.797025i	$0.706406\pi$
$588$		0			0
$589$	32.8559			1.35380
$590$	0.0990106	+	0.0789583i	0.00407620	+	0.00325066i
$591$		0			0
$592$	6.20187	+	27.1722i	0.254895	+	1.11677i
$593$	33.7375	+	16.2471i	1.38543	+	0.667190i	0.970151	−	0.242502i	$-0.0779680\pi$
$593$	33.7375	+	16.2471i	1.38543	+	0.667190i	0.415284	+	0.909692i	$0.363682\pi$
$594$		0			0
$595$	−15.6842	+	11.4806i	−0.642989	+	0.470659i
$596$	−8.83850	+	18.3533i	−0.362039	+	0.751782i
$597$		0			0
$598$	−0.0283277	−	0.0588230i	−0.00115840	−	0.00240545i
$599$	−22.5664	−	17.9961i	−0.922037	−	0.735300i	0.0425421	−	0.999095i	$-0.486454\pi$
$599$	−22.5664	−	17.9961i	−0.922037	−	0.735300i	−0.964579	+	0.263795i	$0.915026\pi$
$600$		0			0
$601$	17.0095	+	13.5646i	0.693832	+	0.553313i	0.905665	−	0.423993i	$-0.139372\pi$
$601$	17.0095	+	13.5646i	0.693832	+	0.553313i	−0.211833	+	0.977306i	$0.567943\pi$
$602$	−0.00100007		0.000533589i	−4.07600e−5		2.17475e-5i
$603$		0			0
$604$	15.1140	−	7.27853i	0.614981	−	0.296159i
$605$	−3.39258	+	14.8639i	−0.137928	+	0.604301i
$606$		0			0
$607$			1.99217i			0.0808597i	0.999182	+	0.0404299i	$0.0128727\pi$
$607$			1.99217i			0.0808597i	−0.999182	+	0.0404299i	$0.987127\pi$
$608$	0.0949761	−	0.416118i	0.00385179	−	0.0168758i
$609$		0			0
$610$	0.0210283	+	0.0921310i	0.000851411	+	0.00373027i
$611$	−7.67403	+	1.75155i	−0.310458	+	0.0708600i
$612$		0			0
$613$	27.5141	+	34.5016i	1.11128	+	1.39351i	0.910319	+	0.413907i	$0.135836\pi$
$613$	27.5141	+	34.5016i	1.11128	+	1.39351i	0.200964	+	0.979599i	$0.435592\pi$
$614$	0.0210267	+	0.0921239i	0.000848568	+	0.00371782i
$615$		0			0
$616$	0.117248	−	0.0217081i	0.00472407	−	0.000874643i
$617$	−30.1981	−	6.89252i	−1.21573	−	0.277482i	−0.433892	−	0.900965i	$-0.642860\pi$
$617$	−30.1981	−	6.89252i	−1.21573	−	0.277482i	−0.781837	+	0.623483i	$0.785717\pi$
$618$		0			0
$619$		−	46.2835i		−	1.86029i	−0.367191	−	0.930145i	$-0.619681\pi$
$619$		−	46.2835i		−	1.86029i	0.367191	−	0.930145i	$-0.380319\pi$
$620$	−22.0954	−	5.04313i	−0.887372	−	0.202537i
$621$		0			0
$622$	−0.0982547	+	0.0783555i	−0.00393966	+	0.00314177i
$623$	−8.16729	−	18.9220i	−0.327215	−	0.758093i
$624$		0			0
$625$	5.24424	−	22.9765i	0.209770	−	0.919061i
$626$	−0.0409074	+	0.0512962i	−0.00163499	+	0.00205021i
$627$		0			0
$628$	6.93782	−	5.53273i	0.276849	−	0.220780i
$629$	−21.2106	−	10.2145i	−0.845722	−	0.407278i
$630$		0			0
$631$	−16.5277	+	7.95934i	−0.657959	+	0.316856i	−0.732905	−	0.680331i	$-0.761836\pi$
$631$	−16.5277	+	7.95934i	−0.657959	+	0.316856i	0.0749456	+	0.997188i	$0.476122\pi$
$632$	0.0518390	−	0.107645i	0.00206204	−	0.00428188i
$633$		0			0
$634$	0.0177154	+	0.00853129i	0.000703568	+	0.000338821i
$635$	9.06748	−	11.3703i	0.359832	−	0.451215i
$636$		0			0
$637$	−3.55085	−	9.26061i	−0.140690	−	0.366919i
$638$		−	0.0632593i		−	0.00250446i
$639$		0			0
$640$	−0.170322	+	0.353676i	−0.00673255	+	0.0139803i
$641$	35.5468	−	8.11333i	1.40401	−	0.320457i	0.547598	−	0.836742i	$-0.315542\pi$
$641$	35.5468	−	8.11333i	1.40401	−	0.320457i	0.856417	+	0.516285i	$0.172685\pi$
$642$		0			0
$643$	6.23020	+	12.9371i	0.245695	+	0.510191i	0.986949	−	0.161034i	$-0.0514828\pi$
$643$	6.23020	+	12.9371i	0.245695	+	0.510191i	−0.741254	+	0.671225i	$0.765769\pi$
$644$	7.86799	+	42.4961i	0.310042	+	1.67458i
$645$		0			0
$646$	0.0749258	+	0.0939540i	0.00294792	+	0.00369657i
$647$	−29.3751	+	14.1463i	−1.15485	+	0.556148i	−0.910488	−	0.413535i	$-0.864294\pi$
$647$	−29.3751	+	14.1463i	−1.15485	+	0.556148i	−0.244365	+	0.969683i	$0.578580\pi$
$648$		0			0
$649$	−20.0994	−	4.58757i	−0.788972	−	0.180078i
$650$	0.00135437	−	0.00169833i	5.31229e−5	−	6.66140e-5i
$651$		0			0
$652$	−27.0102	−	33.8697i	−1.05780	−	1.32644i
$653$	0.582912	+	1.21043i	0.0228111	+	0.0473677i	0.912063	−	0.410050i	$-0.134489\pi$
$653$	0.582912	+	1.21043i	0.0228111	+	0.0473677i	−0.889252	+	0.457418i	$0.848774\pi$
$654$		0			0
$655$	−41.1871			−1.60931
$656$	−44.2874			−1.72913
$657$		0			0
$658$	−0.0828542	−	0.00342603i	−0.00322999	−	0.000133560i
$659$	−17.0491	+	3.89134i	−0.664138	+	0.151585i	−0.541284	−	0.840840i	$-0.682062\pi$
$659$	−17.0491	+	3.89134i	−0.664138	+	0.151585i	−0.122854	+	0.992425i	$0.539205\pi$
$660$		0			0
$661$	37.0956	−	29.5827i	1.44285	−	1.15063i	0.481113	−	0.876658i	$-0.340233\pi$
$661$	37.0956	−	29.5827i	1.44285	−	1.15063i	0.961737	−	0.273976i	$-0.0883389\pi$
$662$	0.0126298	−	0.0100720i	0.000490873	−	0.000391458i
$663$		0			0
$664$	−0.0428005	+	0.00976893i	−0.00166098	+	0.000379108i
$665$	−23.7668	+	27.3991i	−0.921636	+	1.06249i
$666$		0			0
$667$	45.8564			1.77557
$668$	−21.7074			−0.839884
$669$		0			0
$670$	−0.0477798	−	0.0992159i	−0.00184590	−	0.00383304i
$671$	−9.59192	−	12.0279i	−0.370292	−	0.464332i
$672$		0			0
$673$	29.6815	−	37.2194i	1.14414	−	1.43470i	0.261157	−	0.965296i	$-0.415896\pi$
$673$	29.6815	−	37.2194i	1.14414	−	1.43470i	0.882981	−	0.469408i	$-0.155533\pi$
$674$	−0.0734756	−	0.0167703i	−0.00283017	−	0.000645969i
$675$		0			0
$676$	−19.8075	+	9.53878i	−0.761826	+	0.366876i
$677$	20.2146	+	25.3483i	0.776909	+	0.974214i	1.00000		0.000584095i	$-0.000185923\pi$
$677$	20.2146	+	25.3483i	0.776909	+	0.974214i	−0.223090	+	0.974798i	$0.571614\pi$
$678$		0			0
$679$	−0.0586307	+	0.215425i	−0.00225004	+	0.00826727i
$680$	−0.0719323	−	0.149369i	−0.00275848	−	0.00572804i
$681$		0			0
$682$	−0.0572464	+	0.0130661i	−0.00219208	+	0.000500328i
$683$	−11.1029	+	23.0554i	−0.424840	+	0.882189i	0.573189	+	0.819423i	$0.305706\pi$
$683$	−11.1029	+	23.0554i	−0.424840	+	0.882189i	−0.998028	+	0.0627652i	$0.980008\pi$
$684$		0			0
$685$		−	36.8697i		−	1.40872i
$686$	−0.0104749	−	0.103960i	−0.000399934	−	0.00396922i
$687$		0			0
$688$	−0.189380	+	0.237475i	−0.00722006	+	0.00905367i
$689$	−0.968357	−	0.466336i	−0.0368915	−	0.0177660i
$690$		0			0
$691$	−7.95316	+	16.5149i	−0.302552	+	0.628257i	−0.995710	−	0.0925295i	$-0.970505\pi$
$691$	−7.95316	+	16.5149i	−0.302552	+	0.628257i	0.693157	+	0.720786i	$0.256219\pi$
$692$	−33.9367	+	16.3431i	−1.29008	+	0.621270i
$693$		0			0
$694$	−0.150365	−	0.0724119i	−0.00570777	−	0.00274872i
$695$	25.5520	−	20.3771i	0.969244	−	0.772946i
$696$		0			0
$697$	23.3239	−	29.2472i	0.883455	−	1.10782i
$698$	0.0106016	−	0.0464488i	0.000401278	−	0.00175811i
$699$		0			0
$700$	−1.16031	+	0.849327i	−0.0438554	+	0.0321015i
$701$	−4.02702	+	3.21144i	−0.152098	+	0.121294i	−0.696582	−	0.717477i	$-0.745297\pi$
$701$	−4.02702	+	3.21144i	−0.152098	+	0.121294i	0.544484	+	0.838771i	$0.316726\pi$
$702$		0			0
$703$	−42.8295	−	9.77556i	−1.61535	−	0.368692i
$704$		−	15.9755i		−	0.602101i
$705$		0			0
$706$	−0.0190059	−	0.00433798i	−0.000715297	−	0.000163262i
$707$	−11.3273	−	9.82558i	−0.426006	−	0.369529i
$708$		0			0
$709$	1.59463	+	6.98652i	0.0598875	+	0.262384i	0.996004	−	0.0893049i	$-0.0284646\pi$
$709$	1.59463	+	6.98652i	0.0598875	+	0.262384i	−0.936117	+	0.351689i	$0.885607\pi$
$710$	0.112332	+	0.140859i	0.00421573	+	0.00528636i
$711$		0			0
$712$	0.171379	−	0.0391162i	0.00642271	−	0.00146594i
$713$	−9.47158	−	41.4977i	−0.354714	−	1.55410i
$714$		0			0
$715$	1.36917	−	5.99870i	0.0512039	−	0.224339i
$716$			16.2503i			0.607303i
$717$		0			0
$718$	0.00220294	−	0.00965172i	8.22131e−5	−	0.000360199i
$719$	16.5077	−	7.94970i	0.615634	−	0.296474i	−0.0999587	−	0.994992i	$-0.531871\pi$
$719$	16.5077	−	7.94970i	0.615634	−	0.296474i	0.715593	+	0.698518i	$0.246157\pi$
$720$		0			0
$721$	−15.0121	+	17.3065i	−0.559081	+	0.644527i
$722$	0.0915176	+	0.0729828i	0.00340593	+	0.00271614i
$723$		0			0
$724$	−1.24237	−	0.990754i	−0.0461722	−	0.0368211i
$725$	0.661981	+	1.37462i	0.0245853	+	0.0510520i
$726$		0			0
$727$	−0.660640	+	1.37183i	−0.0245018	+	0.0508785i	−0.912861	−	0.408272i	$-0.866132\pi$
$727$	−0.660640	+	1.37183i	−0.0245018	+	0.0508785i	0.888359	+	0.459150i	$0.151846\pi$
$728$	0.0831817	−	0.0154008i	0.00308292	−	0.000570790i
$729$		0			0
$730$	0.0313193	+	0.0150826i	0.00115918	+	0.000558231i
$731$	−0.0570910	−	0.250132i	−0.00211159	−	0.00925147i
$732$		0			0
$733$	17.7905	+	14.1874i	0.657106	+	0.524025i	0.894317	−	0.447434i	$-0.147662\pi$
$733$	17.7905	+	14.1874i	0.657106	+	0.524025i	−0.237211	+	0.971458i	$0.576233\pi$
$734$	0.131092			0.00483868
$735$		0			0
$736$	−0.552945			−0.0203818
$737$	14.0161	+	11.1775i	0.516290	+	0.411728i
$738$		0			0
$739$	1.29406	+	5.66966i	0.0476029	+	0.208562i	0.993136	−	0.116963i	$-0.0373160\pi$
$739$	1.29406	+	5.66966i	0.0476029	+	0.208562i	−0.945533	+	0.325525i	$0.894459\pi$
$740$	27.3021	+	13.1480i	1.00364	+	0.483330i
$741$		0			0
$742$	−0.00855343	−	0.00741948i	−0.000314006	−	0.000272378i
$743$	−6.53479	+	13.5696i	−0.239738	+	0.497821i	−0.985772	−	0.168086i	$-0.946241\pi$
$743$	−6.53479	+	13.5696i	−0.239738	+	0.497821i	0.746034	+	0.665908i	$0.231956\pi$
$744$		0			0
$745$	9.60961	+	19.9546i	0.352069	+	0.731079i
$746$	0.0524288	+	0.0418105i	0.00191955	+	0.00153079i
$747$		0			0
$748$	10.5505	+	8.41376i	0.385765	+	0.307637i
$749$	−2.23440	+	0.964433i	−0.0816432	+	0.0352396i
$750$		0			0
$751$	−21.3873	+	10.2996i	−0.780435	+	0.375838i	−0.781295	−	0.624162i	$-0.785441\pi$
$751$	−21.3873	+	10.2996i	−0.780435	+	0.375838i	0.000859983		1.00000i	$0.499726\pi$
$752$	−4.94462	+	21.6638i	−0.180312	+	0.789998i
$753$		0			0
$754$		−	0.0448792i		−	0.00163440i
$755$	4.05852	−	17.7816i	0.147705	−	0.647137i
$756$		0			0
$757$	4.66663	+	20.4458i	0.169612	+	0.743117i	0.986154	+	0.165832i	$0.0530308\pi$
$757$	4.66663	+	20.4458i	0.169612	+	0.743117i	−0.816543	+	0.577285i	$0.804112\pi$
$758$	−0.0501452	+	0.0114453i	−0.00182135	+	0.000415712i
$759$		0			0
$760$	−0.192889	−	0.241875i	−0.00699682	−	0.00877374i
$761$	−6.54605	−	28.6801i	−0.237294	−	1.03965i	−0.943428	−	0.331576i	$-0.892420\pi$
$761$	−6.54605	−	28.6801i	−0.237294	−	1.03965i	0.706134	−	0.708078i	$-0.250438\pi$
$762$		0			0
$763$	0.980476	−	0.717695i	0.0354956	−	0.0259823i
$764$	13.3722	+	3.05211i	0.483788	+	0.110422i
$765$		0			0
$766$		−	0.157246i		−	0.00568153i
$767$	−14.2595	−	3.25464i	−0.514882	−	0.117518i
$768$		0			0
$769$	38.7385	−	30.8929i	1.39695	−	1.11403i	0.418338	−	0.908291i	$-0.362613\pi$
$769$	38.7385	−	30.8929i	1.39695	−	1.11403i	0.978608	−	0.205735i	$-0.0659586\pi$
$770$	0.0305139	−	0.0571904i	0.00109964	−	0.00206100i
$771$		0			0
$772$	−10.7897	+	47.2728i	−0.388330	+	1.70139i
$773$	−22.2514	+	27.9024i	−0.800328	+	1.00358i	0.199392	+	0.979920i	$0.436103\pi$
$773$	−22.2514	+	27.9024i	−0.800328	+	1.00358i	−0.999720	+	0.0236603i	$0.992468\pi$
$774$		0			0
$775$	1.10723	−	0.882984i	0.0397728	−	0.0317177i
$776$	−0.00171571		0.000826243i	−6.15905e−5		2.96604e-5i
$777$		0			0
$778$	0.00304746	−	0.00146758i	0.000109257	−	5.26153e-5i
$779$	30.2881	−	62.8940i	1.08518	−	2.25341i
$780$		0			0
$781$	−26.4257	−	12.7259i	−0.945584	−	0.455369i
$782$	0.0970665	−	0.121718i	0.00347109	−	0.00435261i
$783$		0			0
$784$	−27.9031	−	2.31154i	−0.996539	−	0.0825550i
$785$		−	9.64800i		−	0.344352i
$786$		0			0
$787$	−6.38240	+	13.2532i	−0.227508	+	0.472425i	−0.983207	−	0.182494i	$-0.941583\pi$
$787$	−6.38240	+	13.2532i	−0.227508	+	0.472425i	0.755699	+	0.654919i	$0.227297\pi$
$788$	25.7055	−	5.86711i	0.915720	−	0.209007i
$789$		0			0
$790$	−0.0281806	−	0.0585176i	−0.00100262	−	0.00208196i
$791$	33.7282	−	14.5581i	1.19924	−	0.517625i
$792$		0			0
$793$	−6.80498	−	8.53317i	−0.241652	−	0.303022i
$794$	0.140293	−	0.0675613i	0.00497880	−	0.00239766i
$795$		0			0
$796$	−24.1105	−	5.50307i	−0.854575	−	0.195051i
$797$	21.7888	−	27.3224i	0.771801	−	0.967807i	−0.228183	−	0.973618i	$-0.573278\pi$
$797$	21.7888	−	27.3224i	0.771801	−	0.967807i	0.999983	+	0.00581107i	$0.00184973\pi$
$798$		0			0
$799$	−11.7026	−	14.6746i	−0.414009	−	0.519151i
$800$	−0.00798227	−	0.0165754i	−0.000282216	−	0.000586027i
$801$		0			0
$802$	0.137620			0.00485952
$803$	−5.65908			−0.199704
$804$		0			0
$805$	41.4571	+	22.1194i	1.46117	+	0.779607i
$806$	−0.0406134	+	0.00926974i	−0.00143055	+	0.000326513i
$807$		0			0
$808$	0.0999953	−	0.0797436i	0.00351782	−	0.00280537i
$809$	36.8227	−	29.3651i	1.29462	−	1.03242i	0.297645	−	0.954677i	$-0.403799\pi$
$809$	36.8227	−	29.3651i	1.29462	−	1.03242i	0.996973	−	0.0777470i	$-0.0247727\pi$
$810$		0			0
$811$	40.5108	−	9.24633i	1.42253	−	0.324682i	0.559076	−	0.829116i	$-0.311156\pi$
$811$	40.5108	−	9.24633i	1.42253	−	0.324682i	0.863450	+	0.504434i	$0.168299\pi$
$812$	−7.80166	+	28.6655i	−0.273785	+	1.00596i
$813$		0			0
$814$	0.0785114			0.00275182
$815$	−47.1005			−1.64986
$816$		0			0
$817$	−0.207729	−	0.431354i	−0.00726753	−	0.0150912i
$818$	−0.0337881	−	0.0423690i	−0.00118137	−	0.00148140i
$819$		0			0
$820$	−30.0223	+	37.6468i	−1.04842	+	1.31468i
$821$	−34.5435	−	7.88433i	−1.20558	−	0.275165i	−0.427898	−	0.903827i	$-0.640746\pi$
$821$	−34.5435	−	7.88433i	−1.20558	−	0.275165i	−0.777679	+	0.628662i	$0.783603\pi$
$822$		0			0
$823$	11.7532	−	5.66002i	0.409689	−	0.197296i	−0.217676	−	0.976021i	$-0.569848\pi$
$823$	11.7532	−	5.66002i	0.409689	−	0.197296i	0.627365	+	0.778725i	$0.284133\pi$
$824$	−0.121837	−	0.152779i	−0.00424440	−	0.00532230i
$825$		0			0
$826$	−0.135947	−	0.0725346i	−0.00473021	−	0.00252380i
$827$	−15.2882	−	31.7462i	−0.531622	−	1.10392i	−0.977908	−	0.209034i	$-0.932968\pi$
$827$	−15.2882	−	31.7462i	−0.531622	−	1.10392i	0.446287	−	0.894890i	$-0.352746\pi$
$828$		0			0
$829$	−34.4974	+	7.87381i	−1.19814	+	0.273469i	−0.774627	−	0.632419i	$-0.782062\pi$
$829$	−34.4974	+	7.87381i	−1.19814	+	0.273469i	−0.423518	+	0.905888i	$0.639205\pi$
$830$	−0.0103548	+	0.0215020i	−0.000359422	+	0.000746347i
$831$		0			0
$832$		−	11.3338i		−	0.392930i
$833$	16.2216	−	17.2097i	0.562047	−	0.596281i
$834$		0			0
$835$	−14.7151	+	18.4522i	−0.509238	+	0.638564i
$836$	22.6881	+	10.9260i	0.784684	+	0.377884i
$837$		0			0
$838$	−0.0315711	+	0.0655580i	−0.00109060	+	0.00226466i
$839$	6.36467	−	3.06506i	0.219733	−	0.105818i	−0.320779	−	0.947154i	$-0.603945\pi$
$839$	6.36467	−	3.06506i	0.219733	−	0.105818i	0.540512	+	0.841336i	$0.318231\pi$
$840$		0			0
$841$	2.27187	+	1.09407i	0.0783403	+	0.0377267i
$842$	−0.136236	+	0.108644i	−0.00469499	+	0.00374413i
$843$		0			0
$844$	25.2976	−	31.7222i	0.870779	−	1.09192i
$845$	−5.31885	+	23.3034i	−0.182974	+	0.801661i
$846$		0			0
$847$	0.766413	−	18.5347i	0.0263343	−	0.636861i
$848$	−2.37220	+	1.89176i	−0.0814615	+	0.0649634i
$849$		0			0
$850$	0.00504992	+	0.00115261i	0.000173211	+	3.95342e-5i
$851$			56.9126i			1.95094i
$852$		0			0
$853$	−34.9523	−	7.97763i	−1.19674	−	0.273149i	−0.422693	−	0.906273i	$-0.638915\pi$
$853$	−34.9523	−	7.97763i	−1.19674	−	0.273149i	−0.774051	+	0.633124i	$0.781772\pi$
$854$	−0.0455664	−	0.105568i	−0.00155925	−	0.00361248i
$855$		0			0
$856$	−0.00461903	−	0.0202373i	−0.000157875	−	0.000691696i
$857$	−6.55916	−	8.22493i	−0.224057	−	0.280958i	0.657079	−	0.753822i	$-0.271792\pi$
$857$	−6.55916	−	8.22493i	−0.224057	−	0.280958i	−0.881136	+	0.472864i	$0.843220\pi$
$858$		0			0
$859$	30.9867	−	7.07251i	1.05725	−	0.241311i	0.341656	−	0.939825i	$-0.389012\pi$
$859$	30.9867	−	7.07251i	1.05725	−	0.241311i	0.715596	+	0.698514i	$0.246155\pi$
$860$	0.0734870	+	0.321968i	0.00250589	+	0.0109790i
$861$		0			0
$862$	0.00793233	−	0.0347538i	0.000270176	−	0.00118372i
$863$			15.3468i			0.522412i	0.965283	+	0.261206i	$0.0841202\pi$
$863$			15.3468i			0.522412i	−0.965283	+	0.261206i	$0.915880\pi$
$864$		0			0
$865$	−9.11293	+	39.9264i	−0.309849	+	1.35754i
$866$	−0.0464793	+	0.0223832i	−0.00157943	+	0.000760613i
$867$		0			0
$868$	27.5522	+	1.13929i	0.935184	+	0.0386699i
$869$	8.26672	+	6.59249i	0.280429	+	0.223635i
$870$		0			0
$871$	9.94371	+	7.92985i	0.336930	+	0.268693i
$872$	0.00449675	+	0.00933760i	0.000152279	+	0.000316211i
$873$		0			0
$874$	0.126049	−	0.261744i	0.00426369	−	0.00885364i
$875$	−1.25302	+	30.3028i	−0.0423599	+	1.02442i
$876$		0			0
$877$	24.2808	+	11.6930i	0.819906	+	0.394846i	0.796320	−	0.604876i	$-0.206777\pi$
$877$	24.2808	+	11.6930i	0.819906	+	0.394846i	0.0235862	+	0.999722i	$0.492492\pi$
$878$	−0.00379096	−	0.0166093i	−0.000127939	−	0.000560536i
$879$		0			0
$880$	−13.5803	−	10.8299i	−0.457792	−	0.365077i
$881$	8.72065			0.293806			0.146903	−	0.989151i	$-0.453069\pi$
$881$	8.72065			0.293806			0.146903	+	0.989151i	$0.453069\pi$
$882$		0			0
$883$	43.9331			1.47847			0.739233	−	0.673449i	$-0.235188\pi$
$883$	43.9331			1.47847			0.739233	+	0.673449i	$0.235188\pi$
$884$	7.48505	+	5.96913i	0.251749	+	0.200764i
$885$		0			0
$886$	−0.00688801	−	0.0301783i	−0.000231407	−	0.00101386i
$887$	51.2104	+	24.6616i	1.71948	+	0.828056i	0.989491	+	0.144592i	$0.0461871\pi$
$887$	51.2104	+	24.6616i	1.71948	+	0.828056i	0.729985	+	0.683464i	$0.239527\pi$
$888$		0			0
$889$	−8.32979	+	15.6120i	−0.279372	+	0.523611i
$890$	0.0414622	−	0.0860972i	0.00138982	−	0.00288598i
$891$		0			0
$892$	−8.51387	−	17.6792i	−0.285066	−	0.591945i
$893$	−27.3838	−	21.8379i	−0.916366	−	0.730777i
$894$		0			0
$895$	13.8134	+	11.0159i	0.461733	+	0.368220i
$896$	0.125431	−	0.460870i	0.00419037	−	0.0153966i
$897$		0			0
$898$	−0.0220714	+	0.0106290i	−0.000736533	+	0.000354696i
$899$	6.51074	−	28.5254i	0.217145	−	0.951376i
$900$		0			0
$901$		−	2.56288i		−	0.0853820i
$902$	−0.0277608	+	0.121628i	−0.000924334	+	0.00404977i
$903$		0			0
$904$	0.0697240	+	0.305481i	0.00231899	+	0.0101601i
$905$	−1.68437	+	0.384445i	−0.0559902	+	0.0127794i
$906$		0			0
$907$	10.9203	+	13.6936i	0.362602	+	0.454688i	0.929348	−	0.369204i	$-0.120370\pi$
$907$	10.9203	+	13.6936i	0.362602	+	0.454688i	−0.566747	+	0.823892i	$0.691798\pi$
$908$	−0.102254	−	0.448003i	−0.00339341	−	0.0148675i
$909$		0			0
$910$	0.0216480	−	0.0405736i	0.000717625	−	0.00134500i
$911$	43.1521	+	9.84919i	1.42969	+	0.326318i	0.866157	−	0.499773i	$-0.166583\pi$
$911$	43.1521	+	9.84919i	1.42969	+	0.326318i	0.563537	+	0.826091i	$0.309440\pi$
$912$		0			0
$913$		−	3.88520i		−	0.128581i
$914$	0.175359	+	0.0400246i	0.00580037	+	0.00132390i
$915$		0			0
$916$	−21.3576	+	17.0321i	−0.705676	+	0.562758i
$917$	49.2767	−	9.12338i	1.62726	−	0.301280i
$918$		0			0
$919$	−6.82258	+	29.8917i	−0.225056	+	0.986036i	0.728553	+	0.684989i	$0.240193\pi$
$919$	−6.82258	+	29.8917i	−0.225056	+	0.986036i	−0.953609	+	0.301047i	$0.902664\pi$
$920$	−0.249888	+	0.313350i	−0.00823857	+	0.0103308i
$921$		0			0
$922$	−0.0151594	+	0.0120892i	−0.000499248	+	0.000398137i
$923$	−18.7476	−	9.02839i	−0.617086	−	0.297173i
$924$		0			0
$925$	−1.70604	+	0.821587i	−0.0560944	+	0.0270136i
$926$	−0.0328300	+	0.0681721i	−0.00107886	+	0.00224028i
$927$		0			0
$928$	−0.342452	−	0.164916i	−0.0112415	−	0.00541363i
$929$	−3.37043	+	4.22638i	−0.110580	+	0.138663i	−0.834041	−	0.551702i	$-0.813979\pi$
$929$	−3.37043	+	4.22638i	−0.110580	+	0.138663i	0.723461	+	0.690365i	$0.242550\pi$
$930$		0			0
$931$	22.3656	−	38.0452i	0.733003	−	1.24688i
$932$			35.6814i			1.16878i
$933$		0			0
$934$	0.0305129	−	0.0633607i	0.000998413	−	0.00207323i
$935$	14.3041	−	3.26482i	0.467794	−	0.106771i
$936$		0			0
$937$	3.38589	+	7.03087i	0.110612	+	0.229689i	0.948926	−	0.315500i	$-0.102172\pi$
$937$	3.38589	+	7.03087i	0.110612	+	0.229689i	−0.838313	+	0.545189i	$0.816458\pi$
$938$	0.0791416	+	0.108119i	0.00258407	+	0.00353021i
$939$		0			0
$940$	15.0635	+	18.8890i	0.491317	+	0.616092i
$941$	34.3424	−	16.5384i	1.11953	−	0.539137i	0.219782	−	0.975549i	$-0.429465\pi$
$941$	34.3424	−	16.5384i	1.11953	−	0.539137i	0.899747	+	0.436412i	$0.143751\pi$
$942$		0			0
$943$	−88.1677	−	20.1237i	−2.87114	−	0.655318i
$944$	−25.7438	+	32.2818i	−0.837891	+	1.05068i
$945$		0			0
$946$	0.000533477	0	0.000668959i	1.73448e−5	0	2.17497e-5i
$947$	−2.54345	−	5.28154i	−0.0826512	−	0.171627i	0.855547	−	0.517725i	$-0.173221\pi$
$947$	−2.54345	−	5.28154i	−0.0826512	−	0.171627i	−0.938198	+	0.346098i	$0.887507\pi$
$948$		0			0
$949$	−4.01482			−0.130327
$950$	0.00966583			0.000313601
$951$		0			0
$952$	0.119147	+	0.162773i	0.00386159	+	0.00527550i
$953$	−43.7518	+	9.98607i	−1.41726	+	0.323481i	−0.861456	−	0.507832i	$-0.830447\pi$
$953$	−43.7518	+	9.98607i	−1.41726	+	0.323481i	−0.555805	+	0.831313i	$0.687590\pi$
$954$		0			0
$955$	11.6592	−	9.29793i	0.377284	−	0.300874i
$956$	17.4054	−	13.8803i	0.562930	−	0.448922i
$957$		0			0
$958$	0.177331	−	0.0404746i	0.00572930	−	0.00130768i
$959$	8.16703	+	44.1113i	0.263727	+	1.42443i
$960$		0			0
$961$	3.84116			0.123909
$962$	0.0556998			0.00179583
$963$		0			0
$964$	14.9762	+	31.0985i	0.482352	+	1.00161i
$965$	32.8697	+	41.2173i	1.05811	+	1.32683i
$966$		0			0
$967$	4.56688	−	5.72668i	0.146861	−	0.184158i	−0.702960	−	0.711230i	$-0.748139\pi$
$967$	4.56688	−	5.72668i	0.146861	−	0.184158i	0.849821	+	0.527072i	$0.176710\pi$
$968$	0.154259	+	0.0352086i	0.00495808	+	0.00113165i
$969$		0			0
$970$	−0.000932692	0	0.000449161i	−2.99469e−5	0	1.44217e-5i
$971$	3.38600	+	4.24591i	0.108662	+	0.136258i	0.833188	−	0.552989i	$-0.186513\pi$
$971$	3.38600	+	4.24591i	0.108662	+	0.136258i	−0.724527	+	0.689247i	$0.757942\pi$
$972$		0			0
$973$	−26.0570	+	30.0394i	−0.835348	+	0.963018i
$974$	−0.0163703	−	0.0339932i	−0.000524537	−	0.00108921i
$975$		0			0
$976$	−30.0387	+	6.85614i	−0.961516	+	0.219460i
$977$	15.9199	−	33.0581i	0.509324	−	1.05762i	−0.474793	−	0.880098i	$-0.657477\pi$
$977$	15.9199	−	33.0581i	0.509324	−	1.05762i	0.984116	−	0.177524i	$-0.0568088\pi$
$978$		0			0
$979$			15.5569i			0.497200i
$980$	−20.8803	+	22.1522i	−0.666998	+	0.707625i
$981$		0			0
$982$	−0.0479035	+	0.0600691i	−0.00152866	+	0.00191688i
$983$	53.9924	+	26.0014i	1.72209	+	0.829314i	0.988773	+	0.149427i	$0.0477429\pi$
$983$	53.9924	+	26.0014i	1.72209	+	0.829314i	0.733316	+	0.679888i	$0.237971\pi$
$984$		0			0
$985$	12.4381	−	25.8280i	0.396310	−	0.822947i
$986$	0.0964179	−	0.0464324i	0.00307057	−	0.00147871i
$987$		0			0
$988$	16.0960	+	7.75144i	0.512083	+	0.246606i
$989$	−0.484926	+	0.386716i	−0.0154198	+	0.0122968i
$990$		0			0
$991$	−16.0589	+	20.1372i	−0.510128	+	0.639681i	−0.968480	−	0.249090i	$-0.919868\pi$
$991$	−16.0589	+	20.1372i	−0.510128	+	0.639681i	0.458352	+	0.888771i	$0.348440\pi$
$992$	−0.0785076	+	0.343964i	−0.00249262	+	0.0109209i
$993$		0			0
$994$	−0.165596	−	0.143643i	−0.00525240	−	0.00455608i
$995$	−21.0220	+	16.7645i	−0.666443	+	0.531471i
$996$		0			0
$997$	−13.1821	−	3.00872i	−0.417480	−	0.0952872i	0.00862045	−	0.999963i	$-0.497256\pi$
$997$	−13.1821	−	3.00872i	−0.417480	−	0.0952872i	−0.426101	+	0.904676i	$0.640113\pi$
$998$		−	0.239392i		−	0.00757781i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.251.10	yes	120
3.2	odd	2	inner	441.2.w.a.251.11	yes	120
49.41	odd	14	inner	441.2.w.a.188.11	yes	120
147.41	even	14	inner	441.2.w.a.188.10	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.188.10	✓	120	147.41	even	14	inner
441.2.w.a.188.11	yes	120	49.41	odd	14	inner
441.2.w.a.251.10	yes	120	1.1	even	1	trivial
441.2.w.a.251.11	yes	120	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.00441089 - 0.00351757i) q^{2} +(-0.445035 - 1.94982i) q^{4} +(-1.95912 - 0.943460i) q^{5} +(2.55289 + 0.694800i) q^{7} +(-0.00979136 + 0.0203320i) q^{8} +O(q^{10})\)	\(q+(-0.00441089 - 0.00351757i) q^{2} +(-0.445035 - 1.94982i) q^{4} +(-1.95912 - 0.943460i) q^{5} +(2.55289 + 0.694800i) q^{7} +(-0.00979136 + 0.0203320i) q^{8} +(0.00532276 + 0.0110528i) q^{10} +(-1.56142 - 1.24519i) q^{11} +(-1.10775 - 0.883399i) q^{13} +(-0.00881652 - 0.0120447i) q^{14} +(-3.60370 + 1.73545i) q^{16} +(0.751799 - 3.29385i) q^{17} -6.30461i q^{19} +(-0.967708 + 4.23980i) q^{20} +(0.00250721 + 0.0109848i) q^{22} +(-7.96285 + 1.81747i) q^{23} +(-0.169433 - 0.212462i) q^{25} +(0.00177874 + 0.00779316i) q^{26} +(0.218614 - 5.28690i) q^{28} +(-5.47364 - 1.24932i) q^{29} +5.21141i q^{31} +(0.0660021 + 0.0150646i) q^{32} +(-0.0149024 + 0.0118843i) q^{34} +(-4.34589 - 3.76975i) q^{35} +(1.55054 - 6.79337i) q^{37} +(-0.0221769 + 0.0278090i) q^{38} +(0.0383648 - 0.0305949i) q^{40} +(9.97587 + 4.80413i) q^{41} +(0.0684189 - 0.0329488i) q^{43} +(-1.73302 + 3.59865i) q^{44} +(0.0415164 + 0.0199932i) q^{46} +(3.46380 - 4.34347i) q^{47} +(6.03450 + 3.54750i) q^{49} +0.00153314i q^{50} +(-1.22949 + 2.55306i) q^{52} +(0.739555 - 0.168799i) q^{53} +(1.88422 + 3.91261i) q^{55} +(-0.0391230 + 0.0451023i) q^{56} +(0.0197491 + 0.0247646i) q^{58} +(9.30068 - 4.47897i) q^{59} +(7.51004 + 1.71412i) q^{61} +(0.0183315 - 0.0229870i) q^{62} +(4.98744 + 6.25405i) q^{64} +(1.33675 + 2.77580i) q^{65} -8.97651 q^{67} -6.75700 q^{68} +(0.00590892 + 0.0319149i) q^{70} +(14.3180 - 3.26798i) q^{71} +(2.21540 - 1.76672i) q^{73} +(-0.0307354 + 0.0245107i) q^{74} +(-12.2929 + 2.80577i) q^{76} +(-3.12098 - 4.26371i) q^{77} -5.29436 q^{79} +8.69740 q^{80} +(-0.0271036 - 0.0562813i) q^{82} +(1.21293 + 1.52097i) q^{83} +(-4.58047 + 5.74373i) q^{85} +(-0.000417688 - 9.53346e-5i) q^{86} +(0.0406057 - 0.0195547i) q^{88} +(-4.85674 - 6.09016i) q^{89} +(-2.21417 - 3.02489i) q^{91} +(7.08749 + 14.7173i) q^{92} +(-0.0305569 + 0.00697441i) q^{94} +(-5.94815 + 12.3515i) q^{95} +0.0843849i q^{97} +(-0.0141390 - 0.0368744i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 120 * q + 24 * q^4	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Introduction

L-functions

Modular forms

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Database

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